1. Field of the Invention
The present invention relates to fiber optic gyroscopes. More particularly, this invention pertains to apparatus and a method for lowering random walk error in the output of a fiber optic gyroscope.
2. Description of the Prior Art
The Sagnac interferometer is an instrument for determining rotation by measurement of a nonreciprocal phase difference generated between a pair of counterpropagating light beams. It generally comprises a light source such as a laser, an optical waveguide consisting of several mirrors or a plurality of turns of optical fiber, a beamsplitter-combiner, a detector and a signal processor.
In an interferometer, the waves coming out of the beamsplitter counterpropagate along a single optical path. The waveguide is "reciprocal". That is, any distortion of the optical path affects the counterpropagating beams similarly, although the counterpropagating beams will not necessarily experience such perturbations at the same time or in the same direction. Time-varying perturbations may be observed where the time interval is equal to the propagation time of the light around the optical waveguide whereas "nonreciprocal" perturbations affect the counterpropagating beams differently and according to the direction of propagation. Such nonreciprocal perturbations are occasioned by physical effects that disrupt the symmetry of the optical medium through which the two beams propagate.
Two of the nonreciprocal effects are quite well known. The Faraday, or collinear magneto-optic effect, occurs when a magnetic field creates a preferential spin orientation of the electrons in an optical material whereas the Sagnac, or inertial relativistic effect, occurs when rotation of the interferometer with respect to an inertial frame breaks the symmetry of propagation time. The latter effect is employed as the principle of operation of the ring gyroscope.
The measured or detected output of a gyroscope is a "combined" beam (i.e., a composite beam formed of the two counterpropagating beams) after one complete traverse of the gyroscope loop. The rotation rate about the sensitive axis is proportional to the phase shift that occurs between the couterpropagating beams. Accordingly, accurate phase shift measurement is essential.
FIG. 1 is a graph of the well known relationship between the intensity (or power, a function of the square of the electric field) of the detected beam output from the coil of optical fiber and the phase difference that exists between the two counterpropagating beams after completion of a loop transit. (Note: Typically, prior art photodetectors are arranged to measure output power rather than intensity.) The figure discloses a fringe pattern that is proportional to the cosine of the phase difference, .DELTA..phi., between the beams. Such phase difference provides a measure of the nonreciprocal perturbation due, for example, to rotation. A DC level is indicated on FIG. 1. Such DC level corresponds either to the half (average) intensity level or the half power level of the gyro output.
It is a well known consequence of the shape of the fringe pattern, that, when a small phase difference, or a small phase difference .+-.n.pi. where n is an integer, is detected (corresponding to a relatively low rotation rate), the intensity of the output beam will be relatively insensitive to phase deviation or error as the measured phase difference will be located in the region of a maximum or minimum of the output fringe pattern. This phenomenon is illustrated at regions 10, 12, 12', 14 and 14' of the fringe pattern which correspond to phase shifts in the regions of .phi.=0, +2.pi., +.pi., -2.pi. and -.pi. radians respectively. Further, mere intensity does not provide an indication of the sense or direction of the rotation rate.
For the foregoing reasons, an artificially biased phase difference is commonly superimposed upon each of the counterpropagating beams, periodically retarding one and advancing the other in phase as the pair propagates through the sensor coil. The biasing of the phase shift, also known as "nonreciprocal null-shift", enhances the sensitivity of the intensity measurement to phase difference by shifting the operating point to a region characterized by greater sensitivity to a phase deviation .epsilon. indicative of the presence of rotation. In this way, the variation in light intensity observed at the photodetector, .DELTA.I (or power .DELTA.P), is enhanced for a given nonreciprocal phase perturbation .epsilon..
By enhancing the intensity effect due to the presence of a given phase perturbation .epsilon., corresponding increases in photodetector output sensitivity and accuracy are obtained. These, in turn, may be translated into a simplification and resulting economization of the output electronics. Such output electronics commonly includes a differencing circuit for comparing the intensity values of the operating points between which the electro-optic modulator (often a multifunction integrated optical chip or "MIOC") is cycled during a loop transit time .tau..
Presently, fiber optic gyroscopes are commonly biased by a periodic modulation waveform, often either a square wave or a sinusoid. The square wave is cycled between .+-..pi./2 with a period of 2.pi. while the sinusoid is cycled between maxima and minima of approximately .+-.1.8 radians. The sinusoidal extremes correspond to the argument of the maximum of the first order Bessel function of the first kind, J.sub.1 (x). The prior art square wave modulating waveform is illustrated in FIG. 2.
Referring back to FIG. 1, the representative square wave modulation profile of the prior art square wave modulation corresponds to alternation of the output intensity curve between the operating points 16 and 18. Each of the points 16 and 18 lies at an inflection of the intensity fringe pattern where a small nonreciprocal perturbation .epsilon. of the phase difference .DELTA..phi. results in a maximum detectable change, .DELTA.I (.DELTA.P), in the optical intensity (power) output. Also, by alternating the bias imposed between two different operating points, the system can determine the sign of .epsilon. and, thus, the direction of rotation.
In addition to phase modulation, "phase-nulling" is commonly applied to the interferometer output. This introduces an additional phase shift through a negative feedback mechanism to compensate for that due to the nonreciprocal (Sagnac) effect. A phase ramp (either analog or digital) with slope proportional to the rate of change of the measured phase difference is commonly generated for this purpose. Commonly, a ramp, varying in height between 0 and 2.pi. radians, provides the nulling phase shift since the required shift cannot be increased indefinitely due to voltage constraints.
One of the primary uses of inertial systems is to determine aircraft heading. Such a determination depends upon the quality of the system sensors, including the gyros, and is affected by the amount and type of noise in the gyro outputs.
The noise properties of the outputs of advanced technology gyros (e.g., those of the laser and fiber optic type) include a so-called "random walk" characteristic. This represents a stochastic process in which each step constitutes a statistically independent event. When measuring a variable subject to random walk, such as the output of a fiber optic gyroscope, a gradual convergence to a so-called "true" measurement takes place. For example, in measuring the drift rate of heading angle with a fiber optic gyroscope known to possess a true drift rate of 0 degrees per hour, one might expect to obtain a rate measurement of 0.9 degrees per hour over a 100 second time slice and a measurement of 0.3 degrees per hour over a 900 second time slice. It is a characteristic of random walk that the uncertainty of an estimate diminishes as its length (number of samples) is increased.
Random walk can include a random, non-convergent stochastic process known as white noise (i.e., noise whose power spectral density (PSD) is "flat"). The presence of white noise is particularly troublesome when one employs a gyroscope to determine heading angle. When a noise component of gyro output is truly white noise random, the RMS value of the angle will grow with the square root of time. That is, ##EQU1## where:
RW=random walk coefficient;
T=time; and
.sigma.=standard deviation of the heading angle.
The above equation indicates that the random walk error due to white noise will cause the heading angle to grow over time. This, of course, is quite troublesome.
FIG. 3 is a graph (not to scale) that illustrates the relationship that exists between random walk (curve 20) and light source peak power in a fiber optic gyroscope. White noise in the output of a fiber optic gyro can have a number of sources. Electronics noise (both dark current and Johnson or thermal noise), shot noise and beat, or synonymously relative intensity noise, may all contribute. The contributions of electronic noise and shot noise to gyro random walk decrease as the peak power is increased, a phenomenon shown generally in FIG. 3. As may also be seen in that figure, the contribution of synonymously relative intensity noise (curve 22) is independent of peak power and thereby limits the extent to which gyro random walk can be reduced through an increase. In contrast within a predetermined range, increases, in peak power will reduce the contributions of electronics noise (curve 24) and shot noise (curve 26). Beyond such range, increased power will not lead to better random walk performance.
The relative importance of white noise increases with the power of the light source. Superluminescent diodes provide about 0.5 milliwatts of peak power whereas rare earth doped sources are commonly rated in the vicinity of 10 milliwatts. Referring to FIG. 3, the contribution of white noise to random walk is a fraction of that of shot noise which, in turn, is a fraction of that of electronics noise when a low power source, such as a superluminescent diode, is employed. As the power of the light source is increased, the contribution of synonymously relative intensity noise eventually dominates the noise performance of the gyroscope.
A prior art attempt to isolate and remove the effect of white noise from gyro output has involved "tapping" the output of the light source, then differencing such output with that of the gyro. This relies upon the fact that synomously relative intensity noise originates with the light source. The mechanization of such a scheme is complex and fraught with technical difficulties involving synchronization of detected outputs and matching and stabilization of gains with time and temperature as well as a second detector requirement. In addition to the obvious costs, including power, incurred, the size of the gyro is necessarily increased, rendering such approach of limited feasibility.